The usual flat norm F(T) for an n-current T associates T with an n+1 current
S, possibly not unique. Then
F(T)=min{Mass(S)+Mass(T-boundary(S))}=sup(T(phi)), where phi is a smooth
compactly supported n-form with |phi|=<1 and |dphi|=<1. As Mass(S)+Mass(T)
is a quantity of mixed dimensions, the choice of S is not scale invariant.
In effect T-boundary(S) is a smoothed version of T and the amount of
smoothing depends upon scale. If we fix a scale of T we can simulate
rescaling by defining Fa(T)=min{aMass(Sa)+Mass(T-boundary(Sa))}, where phi
is a smooth compactly supported n-form with |phi|=<1 and |dphi|=<a. We
investigate Fa and its associated currents Sa for examples including a
fractal.